Problem 3 Verify that the given differential equation is exact; then solve it. (z + tan¯¹ (y))dy +1+z = 0 y² Solution:

Q: y=X+ Ci ex t %3D

A: Explanation of the answer is as follows

Q: Qui Solve the following ordinary differential equations: x=5y³x³ de 2) (3y³-x¹)dx= 3xy¹dy

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: ential equati x²y dy = C

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Q: Solve the following differential equation: 2 (y+3)dx - xydy = 0

A: If a differential equation can be written as f(x)dx=g(y)dy , then it is known as differential…

Q: - 1 - 1 dx ?

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Q: —у dx + (x+Vху ) dy %3D 0. dy = 0.

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Q: Let W be the subspace of R5 spanned by the vectors = (1,2,3,1,2) and v= (2,4,7,2, -1). A basis of…

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Q: dy = -y + 2 with the initial value y(0) = -2 dx

A: Explanation of the answer is as follows

Q: (1) Solve the following differential equation Solution: 16d¹y dx4 d²y +24- dx2 +9y= 0.

A: Therefore, the required answer is y=(c1​+c2​x)sin(23​x​)+(c3​+c4​x)cos(23​x​)Explanation:Step 1:…

Q: (y + xež) dx – x dy = 0

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Q: 1) Determine whether the differential equation is exact. If it is exact, then solve it. (x³ + y³) dx…

A: Step 1: Step 2: Step 3: Step 4:

Q: QC: Solve the following differential equation: dx² +5dy-6y = 12x - 50sinx dx +

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Q: Solve the given differential equation. All solutions should be found. (9ys + 2x'y) dx – (8xy"+x*) dy…

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Q: Solve the given differential equation by separation of variables. (ey+1)2e-ydx+(ex+1)6e-xdy=0

A: Rearranging the given equation:

Q: Solve y (kx √√3) dx + (√3 − kx) dy O a. 2kx + 4√/31n|kx √3- O b. 2kx + 4√3ln|kx c. 2kx + 4√3 ln | kx…

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Q: Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes through the midpoint…

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Q: Solve the following differential equations. dy a) dx x² +9, y(-4) =0

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Q: 13. The exterior angles of a quadrilateral are y', (y+5)°, (y+10)° and (y+25). Find the value of y.

A: Given that  Exterior angles of the quadrilateral is  y,y+5,y+10 and y+25  To find y